Hard and Soft Constraints for Multi-objective Analog IC Sizing Optimization

In this paper, the constraint handling of the non-dominated sorting genetic algorithm II (NSGA-II) is modified to accommodate for both soft and hard constraints, by introducing the concept of soft-feasible solutions. In this context, soft-feasible solutions are design points that fail to meet the hard constraints (original target specifications) but meet the soft constraints (acceptable relaxation for some of the hard constraints). This soft/hard constraint definition responds to a real-world need since not all constraints have the same relevance and it can be hard to predict reasonable values beforehand. Since analog IC sizing optimization is done on highly constrained search spaces, the proposed methodology increases the capability to retain meaningful soft-feasible elements, hence augmenting diversity when hard-feasibility is difficult to achieve. The proposed methodology was implemented and tested on two circuit topologies, showing improvements of up to 31% on the average dominated hypervolume for difficult but existent target specifications. Moreover, when the target specifications are set to values impossible to be met by the topology, the proposed technique can obtain meaningful performance tradeoffs over the soft-feasible solutions.